Subgroups — C₂×C₅₃×#3177 #27268193

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#541	C₂	1	2	yes	maximal
2	C₅₃×#3177	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#491	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#470	C₂	1	2	yes	maximal
7	C₂×C₅₃×#467	C₂	1	2	yes	maximal
8	C₂×C₅₃×#441	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×Q₁₆×C₅₃	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#405	C₂	1	1	yes	maximal, characteristic
11	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
12	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
15	C₅₃×#541	—	2	8	no	—
16	C₅₃×#541	C₂²	1	16	yes	—
17	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	—
18	C₂×#126×C₅₃	—	2	4	no	—
19	C₂×#125×C₅₃	—	2	4	no	—
20	C₂×#125×C₅₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₅₃	C₂²	1	4	yes	—
23	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#499	C₂²	1	8	yes	complemented
25	C₅₃×#494	C₂²	1	8	yes	complemented
26	C₅₃×#491	C₂²	1	16	yes	complemented
27	C₅₃×#470	C₂²	1	16	yes	—
28	C₅₃×#467	C₂²	1	16	yes	—
29	C₅₃×#441	C₂²	1	16	yes	complemented
30	C₄×Q₁₆×C₅₃	C₂²	1	16	yes	complemented
31	C₂×#107×C₅₃	C₂²	1	2	yes	—
32	C₂×#106×C₅₃	C₂²	1	2	yes	—
33	C₂×#103×C₅₃	C₂²	1	4	yes	—
34	C₂×#103×C₅₃	C₂²	1	4	yes	—
35	C₅₃×#405	C₂²	1	8	yes	—
36	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×Q₈×C₅₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₅₃	—	2	8	no	—
43	C₂×Q₁₆×C₅₃	—	2	8	no	—
44	C₂×Q₁₆×C₅₃	C₂³	1	8	yes	—
45	C₂×Q₁₆×C₅₃	C₂³	1	8	yes	—
46	C₂×M₁₆×C₅₃	—	2	4	no	—
47	C₂×M₁₆×C₅₃	C₂³	1	4	yes	—
48	C₂²×C₈×C₅₃	—	2	4	no	—
49	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
51	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₅₃	—	2	4	no	—
55	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	—
56	#126×C₅₃	—	2	32	no	—
57	#125×C₅₃	—	2	32	no	—
58	#125×C₅₃	—	2	4	no	—
59	#125×C₅₃	C₂³	1	8	yes	—
60	C₂²⋊Q₈×C₅₃	—	2	8	no	—
61	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
62	C₄×Q₈×C₅₃	—	2	8	no	—
63	C₄×Q₈×C₅₃	C₂³	1	16	yes	—
64	#117×C₅₃	D₄	1	4	yes	—
65	#117×C₅₃	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
68	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
70	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₅₃	D₄	1	2	yes	—
74	C₂×C₄²×C₅₃	—	2	4	no	—
75	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
77	#107×C₅₃	C₂³	1	8	yes	—
78	#106×C₅₃	C₂³	1	8	yes	—
79	#103×C₅₃	C₂³	1	16	yes	—
80	#103×C₅₃	C₂³	1	16	yes	—
81	#97×C₅₃	C₂³	1	4	yes	—
82	#97×C₅₃	C₂³	1	4	yes	—
83	C₄×C₈×C₅₃	C₂³	1	4	yes	—
84	C₄×C₈×C₅₃	C₂³	1	4	yes	—
85	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₅₃	—	2	4	no	—
87	C₂×Q₈×C₅₃	—	2	8	no	—
88	C₂×Q₈×C₅₃	—	2	8	no	—
89	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
90	C₂²×C₄×C₅₃	—	2	2	no	—
91	C₂²×C₄×C₅₃	—	2	2	no	—
92	C₂²×C₄×C₅₃	—	2	4	no	—
93	C₂²×C₄×C₅₃	—	2	4	no	—
94	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₅₃	—	2	16	no	—
101	Q₁₆×C₅₃	—	2	16	no	—
102	M₁₆×C₅₃	—	2	8	no	—
103	C₂×C₈×C₅₃	—	2	2	no	—
104	C₂×C₈×C₅₃	—	2	2	no	—
105	C₂×C₈×C₅₃	—	2	8	no	—
106	C₂×C₈×C₅₃	#41	1	4	yes	—
107	C₂×C₈×C₅₃	#41	1	4	yes	—
108	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
109	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
110	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
111	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
112	C₄⋊C₄×C₅₃	—	2	16	no	—
113	C₄⋊C₄×C₅₃	—	2	16	no	—
114	C₄⋊C₄×C₅₃	—	2	16	no	—
115	C₄⋊C₄×C₅₃	—	2	16	no	—
116	C₄⋊C₄×C₅₃	—	2	4	no	—
117	C₄⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
118	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
119	C₂²⋊C₄×C₅₃	—	2	16	no	—
120	C₂²⋊C₄×C₅₃	C₂×D₄	1	8	yes	—
121	C₄²×C₅₃	—	2	16	no	—
122	C₄²×C₅₃	C₂×D₄	1	2	yes	—
123	C₄²×C₅₃	C₂×D₄	1	2	yes	—
124	C₄²×C₅₃	C₂⁴	1	2	yes	—
125	C₄²×C₅₃	C₂⁴	1	2	yes	—
126	C₂³×C₅₃	—	2	2	no	—
127	C₂³×C₅₃	—	2	4	no	—
128	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
129	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₅₃	—	2	8	no	—
131	Q₈×C₅₃	—	2	8	no	—
132	Q₈×C₅₃	—	4	8	no	—
133	C₂×C₄×C₅₃	—	2	2	no	—
134	C₂×C₄×C₅₃	—	2	4	no	—
135	C₂×C₄×C₅₃	—	2	4	no	—
136	C₂×C₄×C₅₃	—	2	4	no	—
137	C₂×C₄×C₅₃	—	2	2	no	—
138	C₂×C₄×C₅₃	—	2	2	no	—
139	C₂×C₄×C₅₃	—	2	8	no	—
140	C₂×C₄×C₅₃	—	2	8	no	—
141	C₂×C₄×C₅₃	—	4	8	no	—
142	C₂×C₄×C₅₃	—	4	8	no	—
143	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
148	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
149	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
150	C₈×C₅₃	—	2	2	no	—
151	C₈×C₅₃	—	2	2	no	—
152	C₈×C₅₃	C₂×#41	1	4	yes	—
153	C₈×C₅₃	C₂×#41	1	4	yes	—
154	C₂×#3177	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₅₃	—	2	2	no	—
156	C₂²×C₅₃	—	2	4	no	—
157	C₂²×C₅₃	—	4	4	no	—
158	C₂²×C₅₃	#532	1	2	yes	—
159	C₂²×C₅₃	#578	1	4	yes	—
160	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
161	C₄×C₅₃	—	2	2	no	—
162	C₄×C₅₃	—	2	4	no	—
163	C₄×C₅₃	—	2	4	no	—
164	C₄×C₅₃	—	4	8	no	—
165	C₄×C₅₃	—	4	8	no	—
166	C₄×C₅₃	#532	1	2	yes	—
167	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
168	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
169	C₂×#541	C₂×C₅₃	1	2	yes	—
170	#3177	C₂×C₅₃	1	16	yes	direct product factor
171	C₂×#499	C₂×C₅₃	1	1	yes	characteristic, complemented
172	C₂×#494	C₂×C₅₃	1	1	yes	characteristic, complemented
173	C₂×#491	C₂×C₅₃	1	2	yes	complemented
174	C₂×#470	C₂×C₅₃	1	2	yes	—
175	C₂×#467	C₂×C₅₃	1	2	yes	—
176	C₂×#441	C₂×C₅₃	1	2	yes	complemented
177	C₂×C₄×Q₁₆	C₂×C₅₃	1	2	yes	complemented
178	C₂×#405	C₂×C₅₃	1	1	yes	characteristic
179	C₂×C₅₃	—	4	2	no	—
180	C₂×C₅₃	#3177	1	4	yes	direct product factor
181	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
182	C₂×C₅₃	C₂×#578	1	2	yes	—
183	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	—
184	C₂²×Q₁₆	C₂²×C₅₃	1	2	yes	—
185	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
187	#541	—	2	8	no	—
188	#541	C₂²×C₅₃	1	16	yes	—
189	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	—
190	C₂×#126	—	2	4	no	—
191	C₂×#125	—	2	4	no	—
192	C₂×#125	C₂²×C₅₃	1	2	yes	—
193	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	4	yes	—
194	C₂×C₄×Q₈	C₂²×C₅₃	1	4	yes	—
195	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
196	#499	C₂²×C₅₃	1	8	yes	complemented
197	#494	C₂²×C₅₃	1	8	yes	complemented
198	#491	C₂²×C₅₃	1	16	yes	complemented
199	#470	C₂²×C₅₃	1	16	yes	—
200	#467	C₂²×C₅₃	1	16	yes	—
201	#441	C₂²×C₅₃	1	16	yes	complemented
202	C₄×Q₁₆	C₂²×C₅₃	1	16	yes	complemented
203	C₂×#107	C₂²×C₅₃	1	2	yes	—
204	C₂×#106	C₂²×C₅₃	1	2	yes	—
205	C₂×#103	C₂²×C₅₃	1	4	yes	—
206	C₂×#103	C₂²×C₅₃	1	4	yes	—
207	#405	C₂²×C₅₃	1	8	yes	—
208	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
209	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
212	C₅₃	C₂×#3177	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²×Q₈	C₂³×C₅₃	1	4	yes	—
214	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
215	C₂×Q₁₆	—	2	8	no	—
216	C₂×Q₁₆	—	2	8	no	—
217	C₂×Q₁₆	C₂³×C₅₃	1	8	yes	—
218	C₂×Q₁₆	C₂³×C₅₃	1	8	yes	—
219	C₂×M₁₆	—	2	4	no	—
220	C₂×M₁₆	C₂³×C₅₃	1	4	yes	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
224	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	—
229	#126	—	2	32	no	—
230	#125	—	2	32	no	—
231	#125	—	2	4	no	—
232	#125	C₂³×C₅₃	1	8	yes	—
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
235	C₄×Q₈	—	2	8	no	—
236	C₄×Q₈	C₂³×C₅₃	1	16	yes	—
237	#117	D₄×C₅₃	1	4	yes	—
238	#117	C₂³×C₅₃	1	4	yes	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₅₃	1	4	yes	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	D₄×C₅₃	1	2	yes	—
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
250	#107	C₂³×C₅₃	1	8	yes	—
251	#106	C₂³×C₅₃	1	8	yes	—
252	#103	C₂³×C₅₃	1	16	yes	—
253	#103	C₂³×C₅₃	1	16	yes	—
254	#97	C₂³×C₅₃	1	4	yes	—
255	#97	C₂³×C₅₃	1	4	yes	—
256	C₄×C₈	C₂³×C₅₃	1	4	yes	—
257	C₄×C₈	C₂³×C₅₃	1	4	yes	—
258	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
273	Q₁₆	—	2	16	no	—
274	Q₁₆	—	2	16	no	—
275	M₁₆	—	2	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	#41×C₅₃	1	4	yes	—
280	C₂×C₈	#41×C₅₃	1	4	yes	—
281	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
282	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
283	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
284	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
285	C₄⋊C₄	—	2	16	no	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
291	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
292	C₂²⋊C₄	—	2	16	no	—
293	C₂²⋊C₄	C₂×D₄×C₅₃	1	8	yes	—
294	C₄²	—	2	16	no	—
295	C₄²	C₂×D₄×C₅₃	1	2	yes	—
296	C₄²	C₂×D₄×C₅₃	1	2	yes	—
297	C₄²	C₂⁴×C₅₃	1	2	yes	—
298	C₄²	C₂⁴×C₅₃	1	2	yes	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
302	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
303	Q₈	—	2	8	no	—
304	Q₈	—	2	8	no	—
305	Q₈	—	4	8	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
317	C₂×C₄	C₂²×D₄×C₅₃	1	4	yes	—
318	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
319	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
321	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
322	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
323	C₈	—	2	2	no	—
324	C₈	—	2	2	no	—
325	C₈	C₂×#41×C₅₃	1	4	yes	—
326	C₈	C₂×#41×C₅₃	1	4	yes	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	C₅₃×#532	1	2	yes	—
331	C₂²	C₅₃×#578	1	4	yes	—
332	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	8	no	—
337	C₄	—	4	8	no	—
338	C₄	C₅₃×#532	1	2	yes	—
339	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
340	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
341	C₂	—	4	2	no	—
342	C₂	C₅₃×#3177	1	4	yes	direct product factor
343	C₂	C₂×C₅₃×#532	1	1	yes	characteristic
344	C₂	C₂×C₅₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₂⁴×C₅₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×#117×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅₃×#3177	C₂	direct (N × H)
3. C₂×C₅₃×#499	C₂	semidirect
4. C₂×C₅₃×#494	C₂	semidirect
5. C₂×C₅₃×#491	C₂	semidirect
8. C₂×C₅₃×#441	C₂	semidirect
9. C₂×C₄×Q₁₆×C₅₃	C₂	semidirect
24. C₅₃×#499	C₂²	semidirect
25. C₅₃×#494	C₂²	semidirect
26. C₅₃×#491	C₂²	semidirect
29. C₅₃×#441	C₂²	semidirect
30. C₄×Q₁₆×C₅₃	C₂²	semidirect
154. C₂×#3177	C₅₃	direct (N × H)
170. #3177	C₂×C₅₃	direct (N × H)
171. C₂×#499	C₂×C₅₃	semidirect
172. C₂×#494	C₂×C₅₃	semidirect
173. C₂×#491	C₂×C₅₃	semidirect
176. C₂×#441	C₂×C₅₃	semidirect
177. C₂×C₄×Q₁₆	C₂×C₅₃	semidirect
180. C₂×C₅₃	#3177	direct (N × H)
196. #499	C₂²×C₅₃	semidirect
197. #494	C₂²×C₅₃	semidirect
198. #491	C₂²×C₅₃	semidirect
201. #441	C₂²×C₅₃	semidirect
202. C₄×Q₁₆	C₂²×C₅₃	semidirect
212. C₅₃	C₂×#3177	direct (N × H)
342. C₂	C₅₃×#3177	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₃×#541	2
C₅₃×#3177	2
C₂×C₅₃×#499	2
C₂×C₅₃×#494	2
C₂×C₅₃×#491	2
C₂×C₅₃×#470	2
C₂×C₅₃×#467	2
C₂×C₅₃×#441	2
C₂×C₄×Q₁₆×C₅₃	2
C₂×C₅₃×#405	2
C₂×#3177	53

Subgroups — C2×C53×#3177 #27268193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3177 #27268193